Observational Modeling of the Kolmogorov-Sinai Entropy

Kolmogorov - Sinai Entropy Rate versus Physical Entropy

We elucidate the connection between the Kolmogorov-Sinai entropy rate k and the time evolution of the physical or statistical entropy S. For a large family of chaotic conservative dynamical systems including the simplest ones, the evolution of Sstd for far-from-equilibrium processes includes a stage during which S is a simple linear function of time whose slope is k. We present numerical confir...

Bridging Conceptual Gaps: The Kolmogorov-Sinai Entropy

Kolmogorov-Sinai entropy from the ordinal viewpoint

In the case of ergodicity much of the structure of a one-dimensional time-discrete dynamical system is already determined by its ordinal structure. We generally discuss this phenomenon by considering the distribution of ordinal patterns, which describe the up and down in the orbits of a Borel measurable map on a subset of the real numbers. In particular, we give a natural ordinal description of...

Eigenvalue Estimates Using the Kolmogorov-Sinai Entropy

The scope of this paper is twofold. First, we use the Kolmogorov-Sinai Entropy to estimate lower bounds for dominant eigenvalues of nonnegative matrices. The lower bound is better than the Rayleigh quotient. Second, we use this estimate to give a nontrivial lower bound for the gaps of dominant eigenvalues ofA and A+V.

Kolmogorov–Sinai entropy from recurrence times

Observing how long a dynamical system takes to return to some state is one of the most simple ways to model and quantify its dynamics from data series. This work proposes two formulas to estimate the KS entropy and a lower bound of it, a sort of Shannon’s entropy per unit of time, from the recurrence times of chaotic systems. One formula provides the KS entropy and is more theoretically oriente...

Positive Kolmogorov-Sinai entropy for the Standard map

We prove that the Kolmogorov-Sinai entropy of the Chirikov-Standard map Tλf : (x, y) 7→ (2x − y + λf(x), x) with f(x) = sin(x) with respect to the invariant Lebesgue measure on the two-dimensional torus is bounded below by log(λ/2) − C(λ) with C(λ) = arcsinh(1/λ) + log(2/ √ 3). For λ > λ0 = (8/(6 − 3 √ 3)) = 3.1547..., the entropy of Tλ sin is positive. This result is stable in Banach spaces of...